MLPG_R method for modelling 2D flows of two immiscible fluids

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link City Research OnlineThis article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1002/fld.4353This article is protected by copyright. All rights reserved. MLPG_R method for modelling 2D flows of two immiscible fluids AbstractThis is a first attempt to develop the Meshless Local Petrov-Galerkin method with Rankine source solution (MLPG_R method) to simulate multiphase flows. In this paper, we do not only further develop the MLPG_R method to model two-phase flows but also propose two new techniques to tackle the associated challenges. The first technique is to form an equation for pressure on the explicitly identified interface between different phases by considering the continuity of the pressure and the discontinuity of the pressure gradient (i.e., the ratio of pressure gradient to fluid density), the latter reflecting the fact that the normal velocity is continuous across the interface. The second technique is about solving the algebraic equation for pressure, which gives reasonable solution not only for the cases with low density ratio but also for the cases with very high density ratio, such as more than 1000. The numerical tests show that the results of the newly developed two-phase MLPG_R method agree well with analytical solutions and experimental data in the cases studied.The numerical results also demonstrate that the newly developed method has a second-order convergent rate in the cases for sloshing motion with small amplitudes.

Computation of unsteady generalized Couette flow and heat transfer in immiscible dusty and non‐dusty fluids with viscous heating and wall suction effects using a modified cubic B‐spine differential quadrature method

“…They deployed forward time/central space (FT/CS) finite-difference and Galerkin finite-element methods, observing a strong modification in velocity components with inertial and magnetic field effects. Zhou et al 42 implemented a meshless Local Petrov-Galerkin method with Rankine source solution (MLPG_R method) to compute two-fluid Newtonian flows with both low density and very high density-ratios. Further investigations include McLean et al 43 and Bittleston et al 44 (on primary cement displacement immiscible flows in oil well systems) and Tang et al 45 (on two-and three-dimensional piecewise linear (PLIC) VOF Eulerian grid computation of immiscible twin-screw extruder interfacial flows).…”

Accelerating multi‐dimensional interpolation using moving least‐squares on the GPU

“…As having been introduced, the MLS interpolation has been commonly used as the shape function in various Meshfree methods such as Meshless Local Petrov Galerkin (MLPG) method . Moreover, in most of the application cases when analyzing large‐scale problems using the Meshfree methods, the computational efficiency is usually not practical or satisfactory.…”

“…As having been introduced, the MLS interpolation has been commonly used as the shape function in various Meshfree methods such as Meshless Local Petrov Galerkin (MLPG) method. [28][29][30][31][32] Moreover, in most of the application cases when analyzing large-scale problems using the Meshfree methods, the computational efficiency is usually not practical or satisfactory. Motivated by improving the computational efficiency of the Meshfree methods, we are quite interested in developing efficient MLS interpolation algorithms by exploiting the power of modern programmable GPUs.…”

Standard WCSPH for Free-Surface Multi-Phase Flows with a Large Density Ratio

“…The SPH governing equations holds for each phase, and a coupling condition is imposed at the interface: incompressible (water) phase provides a velocity boundary condition for compressible (air) phase; air phase provides pressure boundary condition at the interface for the water phase. Zhou et al [2016] developed a meshless local Petrov-Galerkin method based on Rankine source (MLPG R method) to deal with 2D two-phase°ow involving°uids with low viscosity and negligible surface tension for which continuity of pressure across the interface can be assumed. The two°uids were considered individually when formulating the governing equations, and a coupling condition was obtained by formulating a novel pressure equation for interface particles.…”